Question

The radius of a right circular cylinder is decreasing at a rate of 2 inches per minute while the height is increasing at a rate of 8 inches per minute. determine the rate of change of the volume when r = 5 and h = 7.

Answer 1

V(t) = πr^2h
V'(t) = π(2rr'h + r^2h')
V'(t) = π(2(5)(-2)(7) + 5^2(8)
V'(t) = π(-140 + 200)
V'(t) = 60π in^3

Answer 2

The volume of the right circular cylinder is 60π cubic inches or 188.50 cubic inches if the radius of a right circular cylinder is decreasing at a rate of 2 inches per minute.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

$\rm V = \pi r^2 h$

After partial differentiation, we get:

V = π(2rr'h + r²h')

r = 5 inches, r' = -2 inches, h = 7 inches, and h' = 8 inches

V = π(2×5×(-2)×7 + (5)²×8)

V = π(-140+200)

V = 60π cubic inches  or

V = 188.50 cubic inches

Thus, the volume of the right circular cylinder is 60π cubic inches or 188.50 cubic inches if the radius of a right circular cylinder is decreasing at a rate of 2 inches per minute.

Learn more about the cylinder here:

brainly.com/question/3216899

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